One of the passages that describes what the second death is can be found in the New Testament, the book of Revelation 21:8 “The cowardly, the unbelieving, the vile, the murderers, the sexually immoral, those who practice magic arts, the idolaters and all liars – their place will be in the fiery lake of burning sulfur. This is the second death.” Essentially, when people are saved they only die an earthly death which the Bible refers to on several occasions as sleep. The saved are not affected by the second death. When an unsaved person dies, (i.e.: someone who has rejected Jesus Christ as their savior) they will await the judgement at which point they will be resurrected to punishment and be cast into the lake of Fire for all eternity.
Although the term is not found in the Hebrew Bible, Sysling in his study (1996) of Teḥiyyat ha-metim (Hebrew; "resurrection of the dead") in the Palestinian Targums identifies a consistent usage of the term "second death" in texts of the Second Temple period and early Rabbinical writings. In most cases this "second death" is identical with the judgment, following resurrection, in Gehinnom at the Last Day.
Targum Isaiah has three occurrences. The first is 22:14 where the Aramaic paraphrases the Hebrew as: “This sin will not be forgiven you until you die the second death.”  The final two examples are from Targum Isaiah 65 which sets the scene for an apocalyptic final battle. Targum Isaiah 65:6 paraphrases the Hebrew in line with the interpretation of the penultimate verse of the Hebrew Isaiah found in the Gospel of Mark where "their worms does not die" is equated with Gehinnom. Here both Targum Isaiah and Gospel of Mark supply the term "Gehinnom", where Hebrew Isaiah simply concludes with the heaps of corpses following the last battle where "their worms do not die" making no further eschatological extension into resurrection and judgment.
Targum Jeremiah 51:17 has the Aramaic "they shall die the second death and not live in the world to come" which appears to depart from the other Targum uses in not being explicit that the second death is after resurrection, but may instead be an exclusion from resurrection.
The majority reading of Targum Psalm 49:11 has the Aramaic translation "For the wise see that the evildoers are judged in Gehinnom". However several manuscripts, including Paris No.10, Montefiore No.7, and Targum of Salomos 113 have the variant Aramaic translation "He sees men wise in wickedness, who die a second death, and are judged in Gehinnom."
The main occurrence of the term "second death" in Christianity are the series of uses in Revelation, 2:11, 20:6, 20:14 and 21:8. There are different interpretations as to the meaning of the term "second death"
The majority of Christians who believe in the immortality of the soul regard the second death to mean eternal suffering or torment in a place called the Lake of Fire, though a minority of Christians who believe in the mortality of the soul teach universal salvation. Mortalists, including some Anglicans, some Lutherans, all Seventh-day Adventists, and others, oppose the idea of eternal suffering but believe that the Second death is an actual second death, meaning that the soul perishes and will be annihilated after the final judgment.
- Harry Sysling Teḥiyyat ha-metim: the resurrection of the dead in the Palestinian Targums p222 1996 -"Here the second death is identical with the judgment in Gehinnom. The wicked will perish and their riches will be given to ... The second death in the Apocalypse In the Apocalypse of John, the second death is mentioned several times. ...
- Sysling, p220
- Martin McNamara, Targum and Testament revisited: Aramaic paraphrases of the Hebrew p.226 2010 - 359
- Sysling Teḥiyyat ha-metim: the resurrection of the dead in the Palestinian Targums p221 1996
- Israel Abrahams Studies in Pharisaism and the Gospels Page 44 "Qimhi's interpretation that the Second Death refers to the " death of the soul in the world to come " cannot be accepted without qualification. For in its paraphrase of Isaiah lxv. 6 the Targum uses the expression : " I will deliver ."